(a)
The distance travelled by Carlos and Shannon when Shannon catches up to Carlos.
(a)
Answer to Problem 172P
The distance travelled by Carlos and Shannon when Shannon catches up to Carlos is
Explanation of Solution
Given that the angle of inclination of the slope is
The forces acting on the system is shown in Figure 1.
Write the equilibrium condition for forces acting on the system in
Apply the condition in equation (I) to the system.
Here,
Write the expression for the force of friction
Here,
Use equation (IV) in (III).
Apply the condition in equation (II) to the system.
Use equation (VI) in (V) and solve for
Write the expression for the distance moved by Shannon when she meet Carlos.
Here,
Write the expression for
Here,
Write the expression for the expression for
Here,
Use equation (IX) and (X) in (VIII).
Write the expression for the speed of the Carlos’s sled when Shannon just begin to move.
Use equation (XII) in (IX).
Solve the quadratic equation (XIII) for
Using equation (VII) write the expression for the acceleration of Carlos and Shannon.
Here,
Deduce
Use equation (XV) and the expression for
Write the expression for the distance travelled by Shannon when she meet Carlos in terms of acceleration of Shannon.
Use the expression for
Conclusion:
Substitute
The negative value obtained as the solution of
Substitute
Therefore, the distance travelled by Carlos and Shannon when Shannon catches up to Carlos is
(b)
The speed with which Shannon moving with respect to Carlos as she pass by.
(b)
Answer to Problem 172P
The speed with which Shannon moving with respect to Carlos as she pass by is
Explanation of Solution
Write the expression for the relative speed between Shannon and Carlos.
Here,
Use equation (XII) and (XV), and the expression for
Conclusion:
Substitute
Therefore, the speed with which Shannon moving with respect to Carlos as she pass by is
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